We present a numerical simulation of the dynamical collapse of a nonrotating , magnetic molecular cloud core and follow the core ’ s evolution through the formation of a central point mass and its subsequent growth to a 1 ~ { } M _ { \odot } protostar .
The epoch of point-mass formation ( PMF ) is investigated by a self-consistent extension of previously presented models of core formation and contraction in axisymmetric , self-gravitating , isothermal , magnetically supported interstellar molecular clouds .
Prior to PMF , the core is dynamically contracting and is not well approximated by a quasistatic equilibrium model .
Ambipolar diffusion , which plays a key role in the early evolution of the core , is unimportant during the dynamical pre-PMF collapse phase .
However , the appearance of a central mass , through its effect on the gravitational field in the inner core regions , leads to a “ revitalization ” of ambipolar diffusion in the weakly ionized gas surrounding the central protostar .
This process is so efficient that it leads to a decoupling of the field from the matter and results in an outward-propagating hydromagnetic C-type shock .
The existence of an ambipolar diffusion-mediated shock of this type was predicted by Li & McKee ( 1996 ) , and we find that the basic shock structure given by their analytic model is well reproduced by our more accurate numerical results .
Our calculation also demonstrates that ambipolar diffusion , rather than Ohmic diffusivity operating in the innermost core region , is the main field decoupling mechanism responsible for driving the shock after PMF .

The passage of the shock leads to a substantial redistribution , by ambipolar diffusion but possibly also by magnetic interchange , of the mass contained within the magnetic flux tubes in the inner core .
In particular , ambipolar diffusion reduces the flux initially threading a collapsing \sim 1 ~ { } M _ { \odot } core by a factor \gtrsim 10 ^ { 3 } by the time this mass accumulates within the inner radius ( \simeq 7.3 ~ { } { AU } ) of our computational grid .
This reduction , which occurs primarily during the post-PMF phase of the collapse , represents a significant step towards the resolution of the protostellar magnetic flux problem .

Our calculations indicate that a 1 ~ { } M _ { \odot } protostar forms in \sim 1.5 \times 10 ^ { 5 } ~ { } yr for typical cloud parameters .
The mass accretion rate is time dependent , in part because of the C-shock that decelerates the infalling matter as it propagates outward : the accretion rate rises to \simeq 9.4 ~ { } M _ { \odot } ~ { } Myr ^ { -1 } early on and decreases to \simeq 5.6 ~ { } M _ { \odot } ~ { } { Myr } ^ { -1 } by the time a solar-mass protostar is formed .
The infalling gas disk surrounding the protostar has a mass \sim 10 ^ { -2 } ~ { } M _ { \odot } at radii r \gtrsim 500 ~ { } AU .
A distinguishing prediction of our model is that the rapid ambipolar diffusion after the formation of a protostar should give rise to large ( \gtrsim 1 ~ { } { km } ~ { } { s } ^ { -1 } ) , and potentially measurable , ion–neutral drift speeds on scales r \lesssim 200 ~ { } AU .

The main features of our simulation , including the C-shock formation after PMF , are captured by a similarity solution that incorporates the effects of ambipolar diffusion ( Contopoulos , Ciolek , & Königl 1997 ) . \keywords accretion , accretion disks — diffusion — ISM : clouds — ISM : magnetic fields — MHD — stars : formation — stars : pre-main-sequence